$($b$)$ Consider homogeneous nucleation in which a spherical solid phase with a radius

$r$ is formed in the liquid phase in the process of forming a solid phase. In this

case, show that the critical radius $r^{**}$ is represented by equation $(1).$

$r^{**}=\frac{2{}_{SL}}{G_V},$

where ${}_{SL}$ is the interfacial energy of the solid phase and the liquid phase per

unit area and $G_V$ is the amount of change in Gibbs energy per unit volume of

solid when the solid phase is transformed into a liquid phase.